The Finger Lakes Feather Club's show in Syracuse is the beginning of June. Norther NY Poultry Fanciers also have a spring show but I'm not exactly sure when. May I think.
There are no sanctioned shows on Lond Island or in Westchester County.
I'd recommend you subscribe to The Poultry Press for information on all the shows in the country.

Only 2 that I know of.
The Queens County fair, and the Bethpage Village fair, I think August and September...
Bethpage is so-so, but Queens is GREAT!
My Clyde got best in show last year, and we will be back again this year.
As far as Long Islanders go, we are geographically unsuitable.
The best "real" chicken show that is closest to us is Sussex County, in Sparta, NJ May 19, and Delmarva in Harrington, DE Mar 31-Apr 1.
Sending you a PM.

This isn't a poultry show, but if you want to see gorgous color paintings of 19th century campions and coops, come to this FREE event at the Horticultural Society of NY on Wednesday, March 7, 6:30 pm. There may be live chickens, too--in midtown!